Matlab Integral function for a self teaching beginner

The integral function numerically integrates the function supplied to it over the variable range defined in the function call. It does not assume matrix data unless you tell it, otherwise assuming scalar data.

Use the trapz function for gridded data —

t=0:1:10;
x=0:1:10;
c = pi;                                     % Create 'c'
[time space]=meshgrid(t,x);
fun=@(c) time+space+c;
answer_cols=trapz(fun(c))
answer_cols = 1×11
   81.4159   91.4159  101.4159  111.4159  121.4159  131.4159  141.4159  151.4159  161.4159  171.4159  181.4159
answer = trapz(answer_cols)
answer = 1.3142e+03

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Bruce Griffin 2022-7-14

what if I need c to be integrated over a different interval such as -inf to inf?

Star Strider 2022-7-14

Use the integral function with the 'ArrayValued' name-value pair.

The integral function and the trapz (or incremental cumtrapz) functions do different things depending on what the data are and what result you want.

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Answer 2

Steven Lord 2022-7-14

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By default, integral calls the integrand function you pass into it with an array of data, not just a scalar. It requires your integrand function to return an array the same size as the input as output. Each element of the output represnts the value of your integrand function at the corresponding element of the input.

In your code:

t=0:1:10;
x=0:1:10;
[time space]=meshgrid(t,x);
fun=@(c) time+space+c;

that would only work if c was compatibly sized with time and space. One example of a c that's compatibly sized is a scalar.

fun(42)
ans = 11×11
  43    44    45    46    47    48    49    50    51    52
  44    45    46    47    48    49    50    51    52    53
  45    46    47    48    49    50    51    52    53    54
  46    47    48    49    50    51    52    53    54    55
  47    48    49    50    51    52    53    54    55    56
  48    49    50    51    52    53    54    55    56    57
  49    50    51    52    53    54    55    56    57    58
  50    51    52    53    54    55    56    57    58    59
  51    52    53    54    55    56    57    58    59    60
  52    53    54    55    56    57    58    59    60    61

One example of a c that's not compatibly sized with time and space is a 1-by-2 vector. Adding an 11-by-11 matrix and a 1-by-2 matrix is not mathematically defined.

fun([42, -1])
Arrays have incompatible sizes for this operation.

Error in solution (line 4)
fun=@(c) time+space+c;

But you have no control over the size of the data with which integral calls your function, unless you explicitly tell it "My function returns an array of data, so just call it with a scalar each time". That's what the 'ArrayValued' name-value argument tells integral if you specify that the value of that name-value argument as 1.